{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Attention on MNIST (Saliency and grad-CAM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets build the mnist model and train it for 5 epochs. It should get to about ~99% test accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "60000 train samples\n",
      "10000 test samples\n",
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 7s - loss: 1.5707 - acc: 0.8966 - val_loss: 1.4873 - val_acc: 0.9751\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 5s - loss: 1.4990 - acc: 0.9639 - val_loss: 1.4796 - val_acc: 0.9814\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 5s - loss: 1.4915 - acc: 0.9706 - val_loss: 1.4776 - val_acc: 0.9837\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 5s - loss: 1.4870 - acc: 0.9747 - val_loss: 1.4763 - val_acc: 0.9849\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 5s - loss: 1.4839 - acc: 0.9777 - val_loss: 1.4741 - val_acc: 0.9870\n",
      "Test loss: 1.47411886559\n",
      "Test accuracy: 0.987\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import numpy as np\n",
    "import keras\n",
    "\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Sequential, Model\n",
    "from keras.layers import Dense, Dropout, Flatten, Activation, Input\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "from keras import backend as K\n",
    "\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 5\n",
    "\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "\n",
    "# the data, shuffled and split between train and test sets\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')\n",
    "\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = keras.utils.to_categorical(y_test, num_classes)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax', name='preds'))\n",
    "\n",
    "model.compile(loss=keras.losses.categorical_crossentropy,\n",
    "              optimizer=keras.optimizers.Adam(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=1,\n",
    "          validation_data=(x_test, y_test))\n",
    "\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saliency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize activation over final dense layer outputs, we need to switch the `softmax` activation out for `linear` since gradient of output node will depend on all the other node activations. Doing this in keras is tricky, so we provide `utils.apply_modifications` to modify network parameters and rebuild the graph.\n",
    "\n",
    "If this swapping is not done, the results might be suboptimal. We will start by swapping out 'softmax' for 'linear' and compare what happens if we dont do this at the end."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets pick an input over which we want to show the attention."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f780569af90>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7918805dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class_idx = 0\n",
    "indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "\n",
    "# pick some random input from here.\n",
    "idx = indices[0]\n",
    "\n",
    "# Lets sanity check the picked image.\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (18, 6)\n",
    "\n",
    "plt.imshow(x_test[idx][..., 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time for saliency visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f77db545950>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77dbb9d110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_saliency\n",
    "from vis.utils import utils\n",
    "from keras import activations\n",
    "\n",
    "# Utility to search for layer index by name. \n",
    "# Alternatively we can specify this as -1 since it corresponds to the last layer.\n",
    "layer_idx = utils.find_layer_idx(model, 'preds')\n",
    "\n",
    "# Swap softmax with linear\n",
    "model.layers[layer_idx].activation = activations.linear\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx])\n",
    "# Plot with 'jet' colormap to visualize as a heatmap.\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To used guided saliency, we need to set `backprop_modifier='guided'`. For rectified saliency or deconv saliency, use `backprop_modifier='relu'`. Lets try these options quickly and see how they compare to vanilla saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77da795bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d9f76b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for modifier in ['guided', 'relu']:\n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx,\n",
    "                               seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "    plt.figure()\n",
    "    plt.title(modifier)\n",
    "    plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both of them look a lot better than vanilla saliency! This in inline with observation in the paper.\n",
    "\n",
    "We can also visualize negative gradients to see the parts of the image that contribute negatively to the output by using `grad_modifier='negate'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f77d8febed0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jvT5ce7yyjoi5EXFbRKyIiOURcUHn9ukRcUtErOr8Oa396QLAxNTkZZAdkj6UmUdLer2k\nD0bE0ZIuknRrZs6XdGvncwBAC/ZY1pm5LjPv7Xz8lKSVkg6RdLqkKzuxKyW9o61JAsBEZ/2CMSLm\nSTpG0l2SZmfmus6XHpc0u6szAwD8WuOyjoipkq6VdGFmPjn8a5mZGvr14a6+b1FELI2IpRufGNVc\nAWDCalTWEbGPhor6a5l5Xefm9RFxcOfrB0u7/vV6Zi7OzMHMHJx5QDemDAATT5N3g4SkyyStzMzP\nDPvSjZIWdj5eKOmG7k8PACA1exfj8ZLOlvRARNzXue0jkj4h6ZqIOEfSTySd2c4UAQB7LOvMvFNS\njPDlN3d3OgCAXWG5OQAUMLbLzdvkLmNtc9m7t3rYPwvXN49u+NS+1tDzF6yy8t++6Z2Nsx9+68XW\n2OfqUivvLJN+SEdaY6+YM8mcyyONs0dufdga+5VbvLyWeXFtM7Lu86jNJd7u2O7zzu2YLuPKGgAK\noKwBoADKGgAKoKwBoADKGgAKoKwBoADKGgAKoKwBoADKGgAKoKwBoADKGgAKGD97g7g2tTi2e69u\nNfMvbx6d+a9PW0MvP++VVv5v3/oPjbN36ARr7Cfk/WsVR+qhxtlNOtAa+yg92Fp+8hJraMnbvsV/\nfO1vZA83x55i5r0tWTw93uvDxZU1ABRAWQNAAZQ1ABRAWQNAAZQ1ABRAWQNAAZQ1ABRAWQNAAZQ1\nABRAWQNAAZQ1ABTQ33uD7DSyA+bY7h4F242se6+6c3GOdYM39CF/t9nKXzH4F42z9572CmvsneZJ\nHdy8rHE2VlpD+/tIOI8X13wz7+6vMbXFsd3nRpsdUAxX1gBQAGUNAAVQ1gBQAGUNAAVQ1gBQAGUN\nAAVQ1gBQAGUNAAVQ1gBQAGUNAAWM7XLzUP8sCd2/xbHdpcnOklp3/Mnm2O5cvtc8+ppHzDXe7v24\n1chuMcd2nynTjay3Cl+aZebdx4BjW4tj43m4sgaAAihrACiAsgaAAihrACiAsgaAAihrACiAsgaA\nAihrACiAsgaAAihrACiAsgaAAsZ2b5B+4u470U9mGFl3D5Q5Zt65H919JNx9SiYZWfeR3+YzZb8W\nx5bYv2Oc4MoaAArYY1lHxNyIuC0iVkTE8oi4oHP7xRGxJiLu6/x3WvvTBYCJqclf7nZI+lBm3hsR\n+0q6JyJu6Xzts5n5qfamBwCQGpR1Zq6TtK7z8VMRsVLSIW1PDADwG9Zr1hExT9Ixku7q3HR+RNwf\nEZdHxLQuzw0A0NG4rCNiqqRrJV2YmU9K+oKkIyUt0NCV96dH+L5FEbE0IpZu/HkXZgwAE1Cjso6I\nfTRU1F/LzOskKTPXZ+bOzHxW0pckHbur783MxZk5mJmDM7n2BoC90uTdICHpMkkrM/Mzw24/eFjs\nDEnLuj89AIDU7N0gx0s6W9IDEXFf57aPSDorIhZISkmrJZ3XygwBAI3eDXKnhv5d8hda0v3pAAB2\nhRWMAFDAxN0bpE1t7zvBWRu9tu/DNvdMwYTElTUAFEBZA0ABlDUAFEBZA0ABlDUAFEBZA0ABlDUA\nFEBZA0ABlDUAFEBZA0ABLFxug7PUuB/Hd/TTI6if7hegy7iyBoACKGsAKICyBoACKGsAKICyBoAC\nKGsAKICyBoACKGsAKICyBoACKGsAKICyBoACIjPH7odFbJT0k1186UBJPxuzifQOxzn+TJRj5Tjb\n89LMnLmn0JiW9YiTiFiamYO9nkfbOM7xZ6IcK8fZe7wMAgAFUNYAUEC/lPXiXk9gjHCc489EOVaO\ns8f64jVrAMDu9cuVNQBgN3pa1hFxakQ8GBEPRcRFvZxL2yJidUQ8EBH3RcTSXs+nWyLi8ojYEBHL\nht02PSJuiYhVnT+n9XKO3TDCcV4cEWs65/S+iDitl3PshoiYGxG3RcSKiFgeERd0bh9X53Q3x9m3\n57RnL4NExICk/5P0FkmPSbpb0lmZuaInE2pZRKyWNJiZ4+q9qhHxJklPS/pyZr6qc9s/S9qcmZ/o\n/E94WmZ+uJfzHK0RjvNiSU9n5qd6ObduioiDJR2cmfdGxL6S7pH0Dknv1zg6p7s5zjPVp+e0l1fW\nx0p6KDMfzsxfSfq6pNN7OB/shcy8XdLmF9x8uqQrOx9fqaEnQWkjHOe4k5nrMvPezsdPSVop6RCN\ns3O6m+PsW70s60MkPTrs88fU53fWKKWkmyPinohY1OvJtGx2Zq7rfPy4pNm9nEzLzo+I+zsvk5R+\naeCFImKepGMk3aVxfE5fcJxSn55TfsE4dt6Yma+R9DZJH+z8tXrcy6HX2cbrW46+IOlISQskrZP0\n6d5Op3siYqqkayVdmJlPDv/aeDqnuzjOvj2nvSzrNZLmDvv80M5t41Jmrun8uUHS9Rp6GWi8Wt95\nTfC51wY39Hg+rcjM9Zm5MzOflfQljZNzGhH7aKjAvpaZ13VuHnfndFfH2c/ntJdlfbek+RFxeES8\nWNJ7Jd3Yw/m0JiKmdH6JoYiYIukUSct2/12l3ShpYefjhZJu6OFcWvNceXWcoXFwTiMiJF0maWVm\nfmbYl8bVOR3pOPv5nPZ0UUznbTGfkzQg6fLM/HjPJtOiiDhCQ1fTkvQiSVeNl2ONiKslnaSh3crW\nS/qopG9IukbSYRraZfHMzCz9y7kRjvMkDf11OSWtlnTesNd1S4qIN0q6Q9IDkp7t3PwRDb2eO27O\n6W6O8yz16TllBSMAFMAvGAGgAMoaAAqgrAGgAMoaAAqgrAGgAMoaAAqgrAGgAMoaAAr4f4DKpl0J\nq7nrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d918ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx], \n",
    "                           backprop_modifier='guided', grad_modifier='negate')\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets try all the classes and show original inputs and their heatmaps side by side. We cannot overlay the heatmap on original image since its grayscale.\n",
    "\n",
    "We will also compare the outputs of guided and rectified or deconv saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8f88350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8da9ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8781990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8370e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d3d47f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d37bda50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d3255550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d2bf5350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d25de590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d202ce50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                                   seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Guided saliency seems to give the best results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## grad-CAM - vanilla, guided, rectified"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These should contain more detail since they use `Conv` or `Pooling` features that contain more spatial detail which is lost in `Dense` layers. The only additional detail compared to saliency is the `penultimate_layer_idx`. This specifies the pre-layer whose gradients should be used. See this paper for technical details: https://arxiv.org/pdf/1610.02391v1.pdf\n",
    "\n",
    "By default, if `penultimate_layer_idx` is not defined, it searches for the nearest pre layer. For our architecture, that would be the `MaxPooling2D` layer after all the `Conv` layers. Lets look at all the visualizations like before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4v/56YyB8kod/8cplYzuaK5nQDNWFry0fOucBzZVfufO7m/EP7deO5yPtcK7v\nzYu/phNv6c1k32uCbff05pb3Xlp278Q78+iXf9oveNvyoZsuPaS9tver9fb9iU68+7i1jk3nuEzf\nDNWFm5YPfaRdF9J5Sb5tz/3bd/irdnjhu+bWyq2d+N6d+CTn2PYJtz1hXeiV03MbsYs6a6/vxHt1\nYeK3eZM8Lr2ituZmqC4Aq6nbSKi1np+kLBN+/OqmA8wDdQEYpS4Ao9QF2LgGf9kiAAAAgEYCAAAA\nMJhGAgAAADCYRgIAAAAwmEYCAAAAMJhGAgAAADBYd/wjw+y47HPN+G//l19ZNnb1z9zTXPu5J/7p\nWDnNgl8/89nN+GH/7e87W/jX1UuGDeqO5UPXdwaLn9Wbzd0rkb353L256Md14i1rXb57M+Ense9k\ny+/uPK7nNh7Xcyc9br3HfNLj1jtnWNB77jYep9u+1l7aOn8G6Z0DPzxhvGXS3Ht65/8k9p5s+d2d\nx/UTa3ls1rJeJmt73AHG44oEAAAAYDCNBAAAAGAwjQQAAABgMI0EAAAAYDCNBAAAAGAwjQQAAABg\nMI0EAAAAYLC1HkTOot3ff+GysYe+v732R095TjO+9ek3NOPnfv+7mvEnXPrUZWP3nPXA5tpamuEc\n/qmvNOM72ssh/bnorfndt3bWtp87/dnd7edHcmgnvlcn3tLL7Y5OvDf3fJK56Gs9y/6mCeK3TLjv\n3qz73mO6byc+ybFb61n2s6T39qX1/OidA73zq+eATvyQTrzzwtp0eyfeqwu9urKWJn1L2ntcW68H\nveOy+xrHe9a6pgKsnCsSAAAAgME0EgAAAIDBNBIAAACAwTQSAAAAgME0EgAAAIDBNBIAAACAwTQS\nAAAAgMEmHdrLOtj7nZ9o3+Gd7fBTckwzft98oRFtxfp2TLQaJtWb3d2b9759wu331vdml7f05r33\n9j3Pesd930Zsrwn33ZvnPum8eIbpnf8tvcewdf4M2Xdv+7d24pO8NZukpsy6SY9767nfe972HpPe\nvntxgPnjigQAAABgMI0EAAAAYDCNBAAAAGAwjQQAAABgMI0EAAAAYDCNBAAAAGAwjQQAAABgsO6w\n4lLKYUn+PAsD12uSM2qtryulvCLJryb5yuJdX1Jr/eBaJQrMjvWtC9s78dZ87t7s7r1XmMuoXm6T\nxqdpkrnna/179Wa+T/q4TmLS332Wz4m2+Xm/0Dt/evHec6P3GN7SiU9ikufttN094fpJHtdJH9NJ\nTfq7z66X5SRsAAAHJUlEQVT5qQvASnUbCVmobr9Ra72klLJXkotLKR9ejP1hrfXVa5ceMKPUBWCU\nugCMUhdgg+o2Emqt1yW5bvHnW0splyc5ZK0TA2aXugCMUheAUeoCbFwr+o6EUsrhSX4wyQWLNz23\nlPLpUsqZpZT7L7PmtFLKRaWUi7bnromSBWbPpHUhuWmdMgXWi7oAjJq8Lty+TpkCQwxuJJRS9kxy\ndpIX1FpvSfKGJN+b5OgsdBr/YGfraq1n1Fq31Vq3bc2uq5AyMCtWoy4k+65bvsDaUxeAUatTF/ZY\nt3yBvkGNhFLK1iw8+d9ea31vktRab6i17qi13pPkTUmOWbs0gVmjLgCj1AVglLoAG1O3kVBKKUne\nkuTyWutrltx+0JK7PSXJpaufHjCL1AVglLoAjFIXYOMaMrXhR5L8UpLPlFI+tXjbS5KcUko5Oguj\nXK5K8qw1yRCYReoCMGqT1IVJRwFOe9Qg38kxX0ObpC7A5jNkasP5ScpOQma9wialLgCj1AVglLoA\nG9eKpjYAAAAAm5tGAgAAADCYRgIAAAAwmEYCAAAAMJhGAgAAADCYRgIAAAAwWHf8I8Bsm2T+t9nh\ny5vlY9PLbZZzZ/runnYCHVunncCcmvXHFWBjcUUCAAAAMJhGAgAAADCYRgIAAAAwmEYCAAAAMJhG\nAgAAADCYRgIAAAAwmEYCAAAAMFipta7fzkr5SpIvLblpvyRfXbcEVkZu45HbeFYztwfVWvdfpW2t\nOXVh1chtPJslN3Vh7chtPHIbj7rwbZvlcVptchvPZsltcF1Y10bCd+y8lItqrdumlkCD3MYjt/HM\ncm7rbZaPhdzGI7fxzHJu622Wj4XcxiO38cxybuttlo+F3MYjt/FMKzcfbQAAAAAG00gAAAAABpt2\nI+GMKe+/RW7jkdt4Zjm39TbLx0Ju45HbeGY5t/U2y8dCbuOR23hmObf1NsvHQm7jkdt4ppLbVL8j\nAQAAAJgv074iAQAAAJgjGgkAAADAYFNpJJRSji+l/HMp5cpSyounkcNySilXlVI+U0r5VCnlohnI\n58xSyo2llEuX3LZvKeXDpZTPL/55/xnK7RWllGsXj9+nSilPmkJeh5VS/raUclkp5bOllOcv3j71\n49bIberHbdrUhRXloy6sPC91YQ6pCyvKR11YeV7qwhya5bqQzFZtUBfGyktdGJrPen9HQillS5LP\nJfnJJNck+WSSU2qtl61rIssopVyVZFut9avTziVJSik/muS2JH9eaz1q8bbfT3JTrfX0xQJ6/1rr\ni2Ykt1ckua3W+ur1zmdJXgclOajWekkpZa8kFyc5McnTM+Xj1sjt5Ez5uE2TurAy6sJYeakLc0Zd\nWBl1Yay81IU5M+t1IZmt2qAujJWXujDQNK5IOCbJlbXWL9Rav5nkL5KcMIU85kKt9WNJbhq5+YQk\nb138+a1ZOIHW3TK5TV2t9bpa6yWLP9+a5PIkh2QGjlsjt81OXVgBdWHl1IW5pC6sgLqwcurCXFIX\nVkBdWDl1YbhpNBIOSXL1kr9fk9kqjDXJh0opF5dSTpt2Mss4oNZ63eLP1yc5YJrJ7MRzSymfXrxk\naSqXS31LKeXwJD+Y5ILM2HEbyS2ZoeM2BerC5Gbq/N6JmTm/1YW5oS5MbqbO752YmfNbXZgbs14X\nktmvDTN1fu/EzJzf6kKbL1v8To+rtT4qyROTPGfxspuZVRc+mzJLMzzfkOR7kxyd5LokfzCtREop\neyY5O8kLaq23LI1N+7jtJLeZOW7slLowmZk5v9UFVpG6MJmZOb/VBVbZ3NSGaZ/fOzEz57e60DeN\nRsK1SQ5b8vdDF2+bCbXWaxf/vDHJ+7JwCdWsuWHxMzLf+qzMjVPO59/UWm+ote6otd6T5E2Z0vEr\npWzNwhPs7bXW9y7ePBPHbWe5zcpxmyJ1YXIzcX7vzKyc3+rC3FEXJjcT5/fOzMr5rS7MnZmuC8lc\n1IaZOL93ZlbOb3VhmGk0Ej6Z5IhSyoNLKfdJ8tQkH5hCHt+hlHLfxS+uSCnlvkmekOTS9qqp+ECS\nUxd/PjXJ+6eYy7186wm26CmZwvErpZQkb0lyea31NUtCUz9uy+U2C8dtytSFyU39/F7OLJzf6sJc\nUhcmN/XzezmzcH6rC3NpZutCMje1Yern93Jm4fxWF1aQT13nqQ1JUhZGUrw2yZYkZ9Za/9u6J7ET\npZTvyULnMEl2SfKOaedWSnlnkuOS7JfkhiQvT3JOkncn+e4kX0pycq113b+sZJncjsvCZTU1yVVJ\nnrXk80Trldfjknw8yWeS3LN480uy8BmiqR63Rm6nZMrHbdrUheHUhbHyUhfmkLownLowVl7qwhya\n1bqQzF5tUBfGyktdGJrPNBoJAAAAwHzyZYsAAADAYBoJAAAAwGAaCQAAAMBgGgkAAADAYBoJAAAA\nwGAaCQAAAMBgGgkAAADAYP8XSwYacYRwlYQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77dbb9d290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d0cfe750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d07638d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d01c92d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c3ca1d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d2c8d350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d1c1c550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wgQJ9odEcYb/3yOwgn1Vg22MKjFXx46vLyeKG4kG+cWhzqXaIH79Xl9fM9lC3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\noAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8f55850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d8492850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d13aa810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_cam\n",
    "\n",
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_cam(model, layer_idx, filter_indices=class_idx, \n",
    "                              seed_input=x_test[idx], backprop_modifier=modifier)        \n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case it appears that saliency is better than grad-CAM as penultimate `MaxPooling2D` layer has `(12, 12)` spatial resolution which is relatively large as compared to input of `(28, 28)`. Is is likely that the conv layer hasnt captured enough high level information and most of that is likely within `dense_4` layer. \n",
    "\n",
    "Here is the model summary for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 24, 24, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 9216)              0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 128)               1179776   \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "preds (Dense)                (None, 10)                1290      \n",
      "_________________________________________________________________\n",
      "activation_1 (Activation)    (None, 10)                0         \n",
      "=================================================================\n",
      "Total params: 1,199,882\n",
      "Trainable params: 1,199,882\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization without swapping softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As alluded at the beginning of the tutorial, we want to compare and see what happens if we didnt swap out softmax for linear activation. Lets try this with guided saliency which gave us the best results so far."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LI48AAAB0KY8AAAB0KY8AAAB0KY8AAAB0KY8AAAB0KY8AAAB0KY8AAAB0KY8AAAB0KY8A\nAAB0KY8AAAB0KY8AAAB0zUx6AOq++rOPHZydaztGnIRJuO3HvreU/4vHX1XKz7UDCtna7euJv1GK\nx85aHGAks4VsdWu1upg/Ynj0tOLSHy7mP/i6wdHHv/P1paXXnfuPtVkeV8jeVls6YmMxf0sh+wPF\ntY8p5guz/1Fx7Q21eJxai38hXjQ4+83//X21xT9Yi9dUby8njDLFWDzyCAAAQFe3PGbmBZl5V2be\nsNtl787MTZl57fx/PzLumADASmY/AjB5Qx55vDAiTt/D5b/XWjtx/r9PL+5YAADf4cKwHwGYqG55\nbK19MSK2LMEsAAB7ZD8CMHkL+Z3Ht2bmdfNPIzl80SYCABjOfgRgiexreTwvIp4SESdGxB0R8bt7\nC2bmOZm5ITM3zMWD+/jlAAAeYZ/2IxH3L9V8AFNln8pja21za21Ha21nRPxJRJz0KNnzW2vrW2vr\nZ+OgfZ0TAOA77Ot+JGL4n7wC4P/bp/KYmWt3e/cVEXHD3rIAAGOwHwFYWt2/ZJuZH41df9bzyMzc\nGBG/ERGnZuaJEdFi159afeOIMwIAK5z9CMDkdctja+2sPVz8oRFmAQDYI/sRgMlbyKutAgAAsEJ0\nH3lk+XnXv/nLSY9Ax8yxxwzO3vu8J5bW/qPX/9fqOKO56sFVpXw+tH2kSQAqMiJmC/m5sQaJiOr9\n4rrh0dOLS394ayl+w1ueMzz8ztoo79pxbu0T7rl6ePazz6utHZuK+cpta/h+ISIijqzF4+7CLB++\ntLb2GS+r5R9Xi3/ztd83PLyhtnZ85eLiJ5xWyN5bXLt6+6p9ny42jzwCAADQpTwCAADQpTwCAADQ\npTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQNTPpAWAa3fSb\nRw3O3viSD444Sd3H7ztycPa8X/qJ0tqrbr6qOg7AMjBbyM6NNsUum4ZHj3xWbekjDyvFn3HJ14eH\nX1IbZcvMnbVPePXzhmePqS0d7zuh+AnHD4++qXLbiohVtXh84OLh2Y/9XG3t4VudXU7dXPyEfy5k\nry+ufXQxv7WQrcwdEXFXMT9ZHnkEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kE\nAACgS3kEAACgS3kEAACgS3kEAACga2bSA8D+YPbytaX876z9+EiTjO/CTc8fnF31l1eNOAnAWFpE\nzE16iHnVOTYOj362uPT6WvzGVzx5cPYZP/n12uInPq+WP6aQvae2dMSfVj9huI/9Si1/z9W1/ON+\nbnj2g7Wl44pbip/w+WL+tEJ2a3Ht1cX8lkJ2W3Ht6uyT5ZFHAAAAupRHAAAAupRHAAAAupRHAAAA\nupRHAAAAupRHAAAAupRHAAAAupRHAAAAupRHAAAAupRHAAAAupRHAAAAumYmPQB1B+TOwdnZPGDE\nSSK2/uQpo639m7/1oVL+RasfGGmS+vU413YU0uOeo6r27zZNegSA/djqYn5bMb9lePTC4tKn1eLP\n/Jv/MzjbDsjS2mf+/UWl/J/nvxTSP1daO+LMWvx1xw3PXlhbOmJNLX7PxuHZK/6mtnacUMz/aDFf\nUd27VL9PC9935e/p2WJ+rphfXB55BAAAoEt5BAAAoEt5BAAAoEt5BAAAoEt5BAAAoEt5BAAAoEt5\nBAAAoEt5BAAAoEt5BAAAoEt5BAAAoEt5BAAAoGtm0gNQ956Lf3xw9sw3fGDESSK++F/+cHB2ru0Y\ncZKIuTbq8iVjH2vFMy97Uyl/fFwz0iQAy0VGxGwhP1fIbi/OUpmjmL/n4trSf/GqYv79g6PntbNL\nS198w+tK+U/fd9fg7H2HnFdaO+LQWvyTxxXCG2trx5XF/PGFbPH8n1aLx4Zi/p7KdbO6uHj1+67y\nfV29D6jcv0xe95HHzDw2M7+QmTdl5o2Z+fPzlx+RmZ/LzFvm/z18/HEBgJXIfgRg8oY8bXV7RPxi\na+3pEXFKRLwlM58eEW+PiMtaa8dHxGXz7wMAjMF+BGDCuuWxtXZHa+2a+bfvjYibI+LoiHh5RFw0\nH7soIs4Ya0gAYGWzHwGYvNIL5mTmuoh4Tux6wvWa1tod8x+6MyLWLOpkAAB7YD8CMBmDy2NmHhIR\nH4+IX2itbd39Y621FhF7fLmSzDwnMzdk5oa5eHBBwwIAK9ti7Ecivr0EkwJMn0HlMTNnY9cd9Uda\na5+Yv3hzZq6d//jaiNjjy1y11s5vra1vra2fjYMWY2YAYAVarP1IxMFLMzDAlBnyaqsZER+KiJtb\na7u/JvOlEfHw6y6fHRGfWvzxAADsRwCWgyF/5/EFEfHaiLg+M6+dv+wdEfGeiPjzzHxDRNweEWeO\nMyIAgP0IwKR1y2Nr7YrY9dd09+TFizsOAMAj2Y8ATF7p1VYBAABYmYY8bZVl5skX3z04e9VrVpXW\nPumgB6rjsAdXPTj8ej//zn9bWvtbbz6qlP+Bf7y1lN9RSgPwneaK+dliflshu7m49odr8VVvGxx9\nc95SWvrKdnIpf9G//tpr3ys//OnS2vGaPb6A797dU7jejzqmtvYhxfytldvj5bW1P1+9fVVuuxER\nhxayJxTXrs5SuR6r9wH7F488AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA\n0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0DUz6QGo23HT1wZnf/1tP1Na+xs/urOU/9pL/7iUXyne\nfMGbBmePPfdvi6t/q5gHYPl6UjE/W8huK659WC3+wE2FcGXuiIvyzFp+w88Ozh7/U/9QWvuWo55d\nyseX1gzPrqstHZ8v5m/dWghXby8/VszXbgMR9xeyf1Nce0sxX71uppdHHgEAAOhSHgEAAOhSHgEA\nAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOiamfQAjGv1\np64q5Z/2qdr6P3TWWwZnZ1+3ubT2Z59xcSn/khtePTi788InlNZuWYrHumu/OTi7o7Y0AAvWImKu\nkJ8tZCvrRkRsKeYPK2THnuX6QvaE4tpH1OLrh+8ZbjnkVcVZiu77TCF8XXHxyvmPiFhdyK4prn15\nMb+1mK/cHu8trl393hjzPmD/4pFHAAAAupRHAAAAupRHAAAAupRHAAAAupRHAAAAupRHAAAAupRH\nAAAAupRHAAAAupRHAAAAupRHAAAAurK1tmRf7LA8op2cL16yrwew3F3ZLoutbUtOeg5YSTKf2CLO\nmfQYy9BsMf+kQnZdce0XFvMVG4v56vXyhOHRmeLd//ZaPOKfC9nPFNe+tZg/rJifK2S3Fdfmkc6P\n1v6pe4P0yCMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMA\nAABdyiMAAABdyiMAAABdM5MeAACA5WCumL+9kN1UXPv6Yn71SNl9yW8bHt1eyFbXLts84toREVtH\nXp+l4JFHAAAAurrlMTOPzcwvZOZNmXljZv78/OXvzsxNmXnt/H8/Mv64AMBKZD8CMHlDnra6PSJ+\nsbV2TWYeGhFXZ+bn5j/2e6219403HgBARNiPAExctzy21u6IiDvm3743M2+OiKPHHgwA4GH2IwCT\nV/qdx8xcFxHPiYgr5y96a2Zel5kXZObhizwbAMAj2I8ATMbg8piZh0TExyPiF1prWyPivIh4SkSc\nGLv+T+Dv7uXzzsnMDZm5YS4eXISRAYCVajH2IxH3L9m8ANNkUHnMzNnYdUf9kdbaJyIiWmubW2s7\nWms7I+JPIuKkPX1ua+381tr61tr62ThoseYGAFaYxdqPRDx26YYGmCJDXm01I+JDEXFza+39u12+\ndrfYKyLihsUfDwDAfgRgORjyaqsviIjXRsT1mXnt/GXviIizMvPEiGgRcVtEvHGUCQEA7EcAJm7I\nq61eERG5hw99evHHAQB4JPsRgMkrvdoqAAAAK9OQp60CADD1Zov51YXsXHHtbcX81mJ+uahe5zBZ\nHnkEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kE\nAACga2bSAwAAsBzMjZyv2Dbi2svJSjlOpoVHHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhS\nHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOjK1trSfbHMb0bE7Xv40JERcfeSDTI5\njnP6rJRjdZzjeVJr7fFL/DVhRbMfcZxTZqUcZ8TKOdZlux9Z0vK41yEyN7TW1k96jrE5zumzUo7V\ncQIrwUq5D3Cc02WlHGfEyjnW5XycnrYKAABAl/IIAABA13Ipj+dPeoAl4jinz0o5VscJrAQr5T7A\ncU6XlXKcESvnWJftcS6L33kEAABgeVsujzwCAACwjE20PGbm6Zn51cy8NTPfPslZxpaZt2Xm9Zl5\nbWZumPQ8iyUzL8jMuzLzht0uOyIzP5eZt8z/e/gkZ1wMeznOd2fmpvlzem1m/sgkZ1wMmXlsZn4h\nM2/KzBsz8+fnL5+qc/ooxzl15xToWyn7kWndi0TYj0zbzy77keV7Tif2tNXMPCAivhYRPxwRGyPi\nyxFxVmvtpokMNLLMvC0i1rfWpupv02TmD0XEfRHx31prz5y/7L0RsaW19p75H8KHt9Z+ZZJzLtRe\njvPdEXFfa+19k5xtMWXm2ohY21q7JjMPjYirI+KMiHhdTNE5fZTjPDOm7JwCj24l7UemdS8SYT8S\nU/azy35k+e5HJvnI40kRcWtr7euttYci4mMR8fIJzsM+aK19MSK2fNfFL4+Ii+bfvih2fRPs1/Zy\nnFOntXZHa+2a+bfvjYibI+LomLJz+ijHCaw89iNTwH5kutiPLF+TLI9HR8Q3dnt/YyzzK2uBWkT8\nVWZenZnnTHqYka1prd0x//adEbFmksOM7K2Zed3800j266dOfLfMXBcRz4mIK2OKz+l3HWfEFJ9T\nYI9W0n5kJe1FIqb4Z9ceTO3PLvuR5XVOvWDO0nlha+25EfHSiHjL/NMOpl7b9bzoaX1J3/Mi4ikR\ncWJE3BERvzvZcRZPZh4SER+PiF9orW3d/WPTdE73cJxTe04BYoXuRSKm62fXHkztzy77keV3TidZ\nHjdFxLG7vX/M/GVTqbW2af7fuyLiktj1NJlptXn+OdwPP5f7rgnPM4rW2ubW2o7W2s6I+JOYknOa\nmbOx6w7sI621T8xfPHXndE/HOa3nFHhUK2Y/ssL2IhFT+LNrT6b1Z5f9yPI8p5Msj1+OiOMz87jM\nPDAiXh0Rl05wntFk5sHzvwQbmXlwRLwkIm549M/ar10aEWfPv312RHxqgrOM5uE7r3mviCk4p5mZ\nEfGhiLi5tfb+3T40Ved0b8c5jecU6FoR+5EVuBeJmLKfXXszjT+77EeW7zmd2KutRkTMv+zsByLi\ngIi4oLV27sSGGVFmPjl2/R++iIiZiPizaTnWzPxoRJwaEUdGxOaI+I2I+GRE/HlEfF9E3B4RZ7bW\n9utf7t7LcZ4au55O0CLitoh4427Pw98vZeYLI+KvI+L6iNg5f/E7Ytfz76fmnD7KcZ4VU3ZOgb6V\nsB+Z5r1IhP1ITNnPLvuR5bsfmWh5BAAAYP/gBXMAAADoUh4BAADoUh4BAADoUh4BAADoUh4BAADo\nUh4BAADoUh4BAADoUh4BAADo+n+WG3NTLy9GjwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c1b37790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c115af50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3BwDwEIs6j0TcN679AKbKospja21Pa+1Qa+3BiHh7RDz9YbLXtta2tNa2zBZ/VQMAwLEs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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c0ed3b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAB7JfgRg8FLvtgoAAMDc1OVlqwAAQ2RXROxI5DPZrNFkvpdryc7Orr2Xs8cT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c0c3ebd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DAQAekPMIwPgt5Gcez8vM78w9jOSoRdsIAGA45xGAJTLf8vieiHhURKyLiFsi4h37C2bm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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c09aebd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LLSL+LjNvzsyzx72YEVvWWntk5u1HI2LZOBczYudk5m0zTyPZqZ868Z0y85CI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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c0938590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d1bb81d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Za4trby/mDy9kK18XB5If7/cYVx4BAADo6pbHzLwwM+/MzOv2uu38zLwtM68e/Pei0Y4J\nAEwz+xGA8RvmyuNFEXH6Pm5/f2vthMF/X1rYsQAAfsZFYT8CMFbd8tha+3pE7FiEWQAA9sl+BGD8\n5vNvHs/JzGsGTyM5bMEmAgAYnv0IwCI50PL44Yh4QkScEBG3R8R79xfMzI2ZuSUzt8zFfQd4dwAA\nD3NA+5GIexdrPoCJckDlsbW2vbX2QGvtwYj4SESc+AjZTa21Da21DbNR+5UEAAD7c6D7kYhVizck\nwAQ5oPKYmUfu9deXRcR1+8sCAIyC/QjA4prpBTLzUxFxSkQ8JjNvjYg/jIhTMvOE2PP7xLdFxOtG\nOCMAMOXsRwDGr1seW2tn7uPmj45gFgCAfbIfARi/+bzaKgAAAFOie+URiPiFNWtK+bP+1eVDZ3c+\n+NPS2nf+0eNL+RX3XVHKA8Bw5sY9wCJZWcyvHT66tbj0h4r5Yx83dPTmLxbX/v1W/ICqbxWy20c2\nxR7VE1WxvL6OXHkEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACg\nS3kEAACgS3kEAACgS3kEAACga2bcA8BycPP5Ty3l/+Yx/3Xo7Bk3v7y09oovXVHKA8DkW1nIri2u\nvaaYf2Ihu7m29I+31/Kvfsnw2Q/Vlo74RjE/W8zvKGQr5z8iYlcxv1TWHj9XHgEAAOhSHgEAAOhS\nHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOiaGfcAMA7/59XP\nKeWveeWflPLf2T03dPaedx9VWntF3F7KA8DkW1vIHl5ce1Uxv7OQ3VZb+uRX1vIXFbL3fLi2duwq\n5qvWFLJ3F9deV8xX159crjwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQ\npTwCAADQpTwCAADQpTwCAADQpTwCAADQNTPuAWChzKz/laGzb/yDvyitvSJrXyqv+vZZQ2d/6X9e\nUVobACbfymJ+fSH79OLalxXza4aPPu2VtaV/XIvHPecXwm8oLr6rmJ8t5u8qZLcW176tmOchrjwC\nAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQ\npTwCAADQNTPuAWB/cqb26Xn839w6dPZ3Vt9VWvuTdx9eyh/xB8P/f5kHSysDwDRYWcyvK2QfV1z7\n4lr8Va8ZPntIbem46MriBzyvkN1aXHt7MV+1o5CtzrKrmOch3R1uZh6dmV/LzBsy8/rMPHdw+7rM\n/Epm3jz487DRjwsATCP7EYDxG+byyO6IeHNr7biIeE5EvD4zj4uI8yLi0tbakyLi0sHfAQBGwX4E\nYMy65bG1dntr7arB23dHxI0RsT4izoj/fx3/4oh46aiGBACmm/0IwPiVXjAnM4+NiGdGxOaIOKK1\ndvvgXXdExBELOhkAwD7YjwCMx9DlMTNXR8QlEfHG1trOvd/XWmsR0fbzcRszc0tmbpmL++Y1LAAw\n3RZiPxJx7yJMCjB5hiqPmTkbe75Rf7K19tnBzdsz88jB+4+MiDv39bGttU2ttQ2ttQ2zsWIhZgYA\nptBC7UciVi3OwAATZphXW82I+GhE3Nhae99e7/pCRJw9ePvsiPj8wo8HAGA/ArAUDPOL9J4XEWdF\nxLWZefXgtrdFxLsi4i8z87UR8b2IeMVoRgQAsB8BGLdueWytXR4RuZ93n7qw4wAAPJz9CMD4lV5t\nFQAAgOk0zNNWYTyOf3Ip/p8P//iIBon40z/6nVL+Ud/+5ogmAYDlaGUx/5Ri/tjho6uLS99zWi3/\n6hFlIyJiRzG/rpD9RnHtu4v56ufArmJ+lGbHPcBe5sZ67648AgAA0KU8AgAA0KU8AgAA0KU8AgAA\n0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0DUz7gGYHgcd96ul/MZP\nf35Ek0Qcd+HrS/ljP/6PI5oEACpmC9m5kU2xx9pCdl1t6dUvqOV3F7L3/H1t7Q+cUoqvPuWHw4/y\n4021WX7t7bX8Td8thHfU1i4b9edjReXrKKI2+8ri2pVP3vFz5REAAIAu5REAAIAu5REAAIAu5REA\nAIAu5REAAIAu5REAAIAu5REAAIAu5REAAIAu5REAAIAu5REAAIAu5REAAICumXEPwPS46T8dVsq/\neNXOEU0ScdTf31/7gNZGMwgAU262mF9KW7ddhexTaks/pxaPr941fPbXTikt/RvnfrmUv+zbpxfS\nTyytXX5cbtpdCBfPUdxWzI9uX7e8zY17gBJXHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhS\nHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOhSHgEAAOiaGfcALG8/ffGJQ2cvffF7i6uvKuYBYNxWFvO7\nR5ifK65dVTnWNbWlH1OLR9w4dHL28meUVv5OPKE2yqcr4eLny0W1eOVxiXhWce2dI86P0igr0K4R\nrj1+rjwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQ\npTwCAADQpTwCAADQNTPuAVjefvC8g4bOPnZm1Qgnifjk3YcPnZ3deX9p7VYdBoAptbuYr27FKuvP\nFteeK+ZXFrLFx+Ufa/GIy4ZOzl19cmnlW2fW1ka5rhJ+em3tuLKYr5zT6vmfJkupMo33PLnyCAAA\nQFe3PGbm0Zn5tcy8ITOvz8xzB7efn5m3ZebVg/9eNPpxAYBpZD8CMH7DXIPdHRFvbq1dlZlrIuLK\nzPzK4H3vb629Z3TjAQBEhP0IwNh1y2Nr7faIuH3w9t2ZeWNErB/1YAAAD7EfARi/0r95zMxjI+KZ\nEbF5cNM5mXlNZl6YmYct8GwAAA9jPwIwHkOXx8xcHRGXRMQbW2s7I+LDEfGEiDgh9vyfwPfu5+M2\nZuaWzNwyF/ctwMgAwLRaiP1IxL2LNi/AJBmqPGbmbOz5Rv3J1tpnIyJaa9tbaw+01h6MiI9ExIn7\n+tjW2qbW2obW2obZWLFQcwMAU2ah9iMRo/3VUQCTaphXW82I+GhE3Nhae99etx+5V+xlUfytNgAA\nw7IfARi/YV5t9XkRcVZEXJuZVw9ue1tEnJmZJ8Se35++LSJeN5IJAQDsRwDGbphXW708InIf7/rS\nwo8DAPBw9iMA41d6tVUAAACm0zBPW4WxeOddx5Xy3/y3xw6dbbdfW5wGAIYxN+L8UnJ3IXtNbelt\n22v5OHz46GnFpWNnMX9zIXtjce2qXYXst4pr7yjml5LK48LeXHkEAACgS3kEAACgS3kEAACgS3kE\nAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgK1tri3Zna3NdOylPXbT7A1jq\nNrdLY2fbkeOeA6ZJ5q+0iI3jHoMFNTvuAfYyU8juHuHaERG7inmm16Zo7Qfd/YgrjwAAAHQpjwAA\nAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHQpjwAAAHRl\na23x7izzhxHxvX286zER8aNFG2R8HOfkmZZjdZyjc0xr7ZcW+T5hqtmPOM4JMy3HGTE9x7pk9yOL\nWh73O0TmltbahnHPMWqOc/JMy7E6TmAaTMv3AMc5WablOCOm51iX8nF62ioAAABdyiMAAABdS6U8\nbhr3AIvEcU6eaTlWxwlMg2n5HuA4J8u0HGfE9Bzrkj3OJfFvHgEAAFjalsqVRwAAAJawsZbHzDw9\nM/8pM7dm5nnjnGXUMnNbZl6bmVdn5pZxz7NQMvPCzLwzM6/b67Z1mfmVzLx58Odh45xxIeznOM/P\nzNsG5/TqzHzROGdcCJl5dGZ+LTNvyMzrM/Pcwe0TdU4f4Tgn7pwCfdOyH5nUvUiE/cik/eyyH1m6\n53RsT1vNzIMi4p8j4gURcWtEXBERZ7bWbhjLQCOWmdsiYkNrbaJ+N01m/uuIuCci/ntr7WmD2y6I\niB2ttXcNfggf1lp76zjnnK/9HOf5EXFPa+0945xtIWXmkRFxZGvtqsxcExFXRsRLI+I1MUHn9BGO\n8xUxYecUeGTTtB+Z1L1IhP1ITNjPLvuRpbsfGeeVxxMjYmtr7ZbW2v0R8emIOGOM83AAWmtfj4gd\nP3fzGRFx8eDti2PPF8Gytp/jnDittdtba1cN3r47Im6MiPUxYef0EY4TmD72IxPAfmSy2I8sXeMs\nj+sj4vt7/f3WWOIP1jy1iPi7zLwyMzeOe5gRO6K1dvvg7Tsi4ohxDjNi52TmNYOnkSzrp078vMw8\nNiKeGRGbY4LP6c8dZ8QEn1Ngn6ZpPzJNe5GICf7ZtQ8T+7PLfmRpnVMvmLN4Tm6tPSsiXhgRrx88\n7WDitT3Pi57Ul/T9cEQ8ISJOiIjbI+K94x1n4WTm6oi4JCLe2Frbuff7Jumc7uM4J/acAsSU7kUi\nJutn1z5M7M8u+5Gld07HWR5vi4ij9/r7UYPbJlJr7bbBn3dGxOdiz9NkJtX2wXO4H3ou951jnmck\nWmvbW2sPtNYejIiPxISc08ycjT3fwD7ZWvvs4OaJO6f7Os5JPafAI5qa/ciU7UUiJvBn175M6s8u\n+5GleU7HWR6viIgnZebjMvPgiHhVRHxhjPOMTGYeOvhHsJGZh0bEb0bEdY/8UcvaFyLi7MHbZ0fE\n58c4y8g89M1r4GUxAec0MzMiPhoRN7bW3rfXuybqnO7vOCfxnAJdU7EfmcK9SMSE/ezan0n82WU/\nsnTP6dhebTUiYvCysx+IiIMi4sLW2jvGNswIZebjY8//4YuImImIP5+UY83MT0XEKRHxmIjYHhF/\nGBF/HRF/GRGPjYjvRcQrWmvL+h937+c4T4k9TydoEbEtIl631/Pwl6XMPDki/ldEXBsRDw5uflvs\nef79xJzTRzjOM2PCzinQNw37kUnei0TYj8SE/eyyH1m6+5GxlkcAAACWBy+YAwAAQJfyCAAAQJfy\nCAAAQJfyCAAAQJfyCAAAQJfyCAAAQJfyCAAAQJfyCAAAQNf/BaZ282G9vDeTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d841cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77d3e94a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7mdd+JOLepZoPYKrMqzy21ra01h5sre2KiHdHxBkPkb2stba2tbZ2Ng6e75wAAD9hvvuR\niMOWbkiAKTKv8piZx+7x1/Mi4tb9ZQEAxsF+BGBpzfQCmfmhiDgrIo7OzDsi4o0RcVZmnh4RLSI2\nRsQrxzgjALDK2Y8ATF63PLbWzt/Hze8dwywAAPtkPwIweQt5tVUAAABWie6VR1a2nZvvLOUvfP1r\nSvk/fuvbB2dPmS2+QEHbVYo/9jOvGJx9/EXfKK29697bSvk3/8XzB2df/sJLS2u/Ze1HS/n3PPlX\nSvld/2dDKQ8w/eYmPcASKR7nN748PHv600pLH/DwVsq3DTk8fOYnSmv/wk1fK+VPfd3GQvojpbVj\n5vdr+TuvGJ699mW1tY8+rZbf+rlaPk4oZJfTr4Cd7u8XrjwCAADQpTwCAADQpTwCAADQpTwCAADQ\npTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQpTwCAADQNTPpAVheDv/TdaX8b8cf\nDM7e/eL7Smvf/w8Hl/Knvv5vB2cfvPfe0tpVj7v4tsHZs0/+tdLan33C1aX8G99Y+39Ex9XGAViB\nWkTMFfKzhWxl3XGrznJMMf+F4dFrn1Zb+jW1eJ76o+Hh362cz4g4vxaPD7+/EH5Obe2d36nl49zC\n2pW5I+KEl9byWx9by8e2QvaQ4to7ivnl9HU9Wa48AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA\n0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0KU8AgAA0DUz6QFY2Q7/03WF7BgHiYgHx7t8ya7t2wdn\nt33sibXFn1CLv+VJV5fy//3YswZnd26+szYMwIo0N+kB5umYYr56nE8aHt16X23pew6t5a+YHZ79\nH7Wl46ZWy8+8dHh25221teMLxfwzCtnCxzAi4v5aPI5+Ti2/9ZJCuPq5zny58ggAAECX8ggAAECX\n8ggAAECX8ggAAECX8ggAAECX8ggAAECX8ggAAECX8ggAAECX8ggAAECX8ggAAECX8ggAAEBXttaW\n7M6OyKPa0/PsJbs/WBEOOLAU//7HH1vKr3vaB0v5Uz/8qsHZk157U2lt9rauXRfb2t056TlgNcn8\nuRZx4aTHWAJHFPMzxfxsMV9xXDF/VCFb/bhUbStkvzXGtSMinlrIVj6GERGH1OJnnVjLX39bIfzp\n2trlY91UyM4V114uLovW/q67H3HlEQAAgC7lEQAAgC7lEQAAgC7lEQAAgC7lEQAAgC7lEQAAgC7l\nEQAAgC7lEQAAgC7lEQAAgC7lEQAAgC7lEQAAgK6ZSQ8Aq96uB0vxh7/t0FJ+6/t2lPIbXvKuwdnn\nf/DflNZuX/56KQ/AT5stZLeNce2IiEMK2bni2rXHrtqWtrp2NT9O1XO0sZA9rrj2F2rxrSfW8s87\nbXj2E1fV1o6nFvOVz4G7i2tXvzYmq3vlMTMflZl/mZm3ZebXM/PVo9uPyszPZubtoz+PHP+4AMBq\nZD8CMHlDnra6MyJe21o7LSLOjIhXZeZpEXFxRFzXWjs5Iq4b/R0AYBzsRwAmrFseW2ubW2tfGb29\nPSI2xO7r2i+IiCtHsSsj4oXjGhIAWN3sRwAmr/SCOZl5QkQ8JSLWRcQxrbXNo3fdGRHHLOpkAAD7\nYD8CMBmDy2NmHh4RV0fEa1prP/ET2K21FhFtP//uwsxcn5nr5+KBBQ0LAKxui7EfibhvCSYFmD6D\nymNmzsbub9QfaK19dHTzlsw8dvT+YyPirn3929baZa21ta21tbNx8GLMDACsQou1H4movWo1ALsN\nebXVjIj3RsSG1trb93jXNRFxwejtCyLizxZ/PAAA+xGA5WDIL8V5RkT8VkR8LTNvHt32hoh4c0Rc\nlZkvj4jvRsSLxzMiAID9CMCkdctja+3zEZH7effZizsOAMDe7EcAJq/0aqsAAACsTkOetgosIwd8\n7qul/FlXvr6Uv+133jU4u/1NO0prH/Hra0r5Xdu3l/IA7Gl2zOvPFbLjnmW1PF5UPuYRu5/JPdTx\nxbWfU4vfen0tf9FZw7OfuKS2dvygmH9GIfvRfuQnbCjmJ8uVRwAAALqURwAAALqURwAAALqURwAA\nALqURwAAALqURwAAALqURwAAALqURwAAALqURwAAALqURwAAALqURwAAALpmJj0AMF6Pvex7pfz7\nfv2Rg7M3/ML/Kq19zpN/p5Q/4PM3l/IA029u0gPsoTLLjrFNwWLZUMw/tpg/rhZ/5vDoi9uVpaWv\nyh/UZnnZHwzPXvH82trlj/tkufIIAABAl/IIAABAl/IIAABAl/IIAABAl/IIAABAl/IIAABAl/II\nAABAl/IIAABAl/IIAABAl/IIAABAl/IIAABA18ykBwDGa+f37ijlrzrv2YOzv3XtR0prb339/aX8\nIz5figMsA7PF/NxYpoC6u4v5bbX4606r5f/V8OhH/svLSkt/8p67Svl7ji+Ejz+0tHbccUItHxuL\n+cXlyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABd\nyiMAAABdM5MeAFheHtxw++Dsb3z7uaW1//wp7ynlX37m7w0P33RLaW1gNcuImC3k58aUhZXsi7X4\n4afV8t/41PDs02tLb//CI0r5/LdtePitb6oNE4cU85PlyiMAAABdyiMAAABdyiMAAABdyiMAAABd\nyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdyiMAAABdM5MeAFi57juvlfLr/vrn\nSvm/f9xhg7NH3lRaGqBgtpCdG9sUUFf5fKx8nkdEbKrFrygu/5JzB0fzRbX9yAU3XlqbZUMlfE5t\n7bi2mJ8sVx4BAADo6pbHzHxUZv5lZt6WmV/PzFePbr8kMzdl5s2j/355/OMCAKuR/QjA5A152urO\niHhta+0rmbkmIr6cmZ8dve8drbW3jm88AICIsB8BmLhueWytbY6IzaO3t2fmhog4btyDAQD8mP0I\nwOSVfuYxM0+IiKdExLrRTRdl5i2ZeXlmHrnIswEA7MV+BGAyBpfHzDw8Iq6OiNe01rZFxKURcVJE\nnB67/0/g2/bz7y7MzPWZuX4uHliEkQGA1Wox9iMR9y7ZvADTZFB5zMzZ2P2N+gOttY9GRLTWtrTW\nHmyt7YqId0fEGfv6t621y1pra1tra2fj4MWaGwBYZRZrPxIx/NcAAfD/DXm11YyI90bEhtba2/e4\n/dg9YudFxK2LPx4AgP0IwHIw5NVWnxERvxURX8vMm0e3vSEizs/M0yOiRcTGiHjlWCYEALAfAZi4\nIa+2+vmIyH2865OLPw4AwN7sRwAmr/RqqwAAAKxOQ562CrBPD279QSl/2SmPKeWPjBtLeYBhWkTM\nTXoIWGaqXxOH1OIb1/Uze/rh0wvZ20pLX5lbarPE2/uRf7SmuPaOYn6yXHkEAACgS3kEAACgS3kE\nAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACga2bSAwAAACvNjmL+\nU7X4D68thA+prR0nFPOV9bcU115ZXHkEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACg\nS3kEAACgS3kEAACgS3kEAACgS3kEAACgS3kEAACgK1trS3dnmd+PiO/u411HR8TWJRtkchzn9Fkt\nx+o4x+fnW2s/u8T3Caua/YjjnDKr5TgjVs+xLtv9yJKWx/0Okbm+tbZ20nOMm+OcPqvlWB0nsBqs\nlu8BjnO6rJbjjFg9x7qcj9PTVgEAAOhSHgEAAOhaLuXxskkPsEQc5/RZLcfqOIHVYLV8D3Cc02W1\nHGfE6jnWZXucy+JnHgEAAFjelsuVRwAAAJaxiZbHzDwnM7+Zmd/KzIsnOcu4ZebGzPxaZt6cmesn\nPc9iyczLM/OuzLx1j9uOyszPZubtoz+PnOSMi2E/x3lJZm4andObM/OXJznjYsjMR2XmX2bmbZn5\n9cx89ej2qTqnD3GcU3dOgb7Vsh+Z1r1IhP3ItD122Y8s33M6saetZuaBEfE3EfGciLgjIr4UEee3\n1m6byEBjlpkbI2Jta22qfjdNZj4rIu6JiD9prT1xdNsfRcTdrbU3jx6Ej2yt/eEk51yo/RznJRFx\nT2vtrZOcbTFl5rERcWxr7SuZuSYivhwRL4yIl8UUndOHOM4Xx5SdU+Chrab9yLTuRSLsR2LKHrvs\nR5bvfmSSVx7PiIhvtda+3Vr7UUR8OCJeMMF5mIfW2g0RcfdP3fyCiLhy9PaVsfuLYEXbz3FOndba\n5tbaV0Zvb4+IDRFxXEzZOX2I4wRWH/uRKWA/Ml3sR5avSZbH4yLie3v8/Y5Y5h+sBWoR8ZnM/HJm\nXjjpYcbsmNba5tHbd0bEMZMcZswuysxbRk8jWdFPnfhpmXlCRDwlItbFFJ/TnzrOiCk+p8A+rab9\nyGrai0RM8WPXPkztY5f9yPI6p14wZ+k8s7X21Ig4NyJeNXrawdRru58XPa0v6XtpRJwUEadHxOaI\neNtkx1k8mXl4RFwdEa9prW3b833TdE73cZxTe04BYpXuRSKm67FrH6b2sct+ZPmd00mWx00R8ag9\n/n786Lap1FrbNPrzroj4WOx+msy02jJ6DvePn8t914TnGYvW2pbW2oOttV0R8e6YknOambOx+xvY\nB1prHx3dPHXndF/HOa3nFHhIq2Y/ssr2IhFT+Ni1L9P62GU/sjzP6STL45ci4uTMPDEzD4qIl0TE\nNROcZ2wy87DRD8FGZh4WEc+NiFsf+l+taNdExAWjty+IiD+b4Cxj8+NvXiPnxRSc08zMiHhvRGxo\nrb19j3dN1Tnd33FO4zkFulbFfmQV7kUipuyxa3+m8bHLfmT5ntOJvdpqRMToZWffGREHRsTlrbU3\nTWyYMcrMx8Tu/8MXETETER+clmPNzA9FxFkRcXREbImIN0bExyPiqoh4dER8NyJe3Fpb0T/cvZ/j\nPCt2P52gRcTGiHjlHs/DX5Ey85kR8VcR8bWI2DW6+Q2x+/n3U3NOH+I4z48pO6dA32rYj0zzXiTC\nfiSm7LHLfmT57kcmWh4BAABYGbxgDgAAAF3KIwAAAF3KIwAAAF3KIwAAAF3KIwAAAF3KIwAAAF3K\nIwAAAF3KIwAAAF3/D0zuHCSuaJGXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f77c2d7ef90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Swap linear back with softmax\n",
    "model.layers[layer_idx].activation = activations.softmax\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "    \n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                               seed_input=x_test[idx], backprop_modifier='guided')\n",
    "\n",
    "    f, ax = plt.subplots(1, 2)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    ax[1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not work as well! \n",
    "\n",
    "It does not work! The reason is that maximizing an output node can be done by minimizing other outputs. Softmax is weird that way. It is the only activation that depends on other node output(s) in the layer."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
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